Mathematics Education: Taking a Clue
From the Recent Technological Revolution
Things that change and things that do not change
In order to set realistic goals it's important to grasp which parameters are under our control and which are not. To put things in perspective, let me recall a story I ran across in several books:
A 15th century German merchant had a son for whom he sought an advanced commercial education. He approached a prominent professor at a university for an advice as to where he should send his child. The professor replied that if the curriculum was to be confined to adding and subtracting, the instruction could be obtained at a German university; but the art of multiplying and dividing might only be acquired in Italy.
Trying to project the situation into the present time we may ponder the changes that befell travelling technology. We may also feel empathy towards a father whose goal is his son's betterment and who's about to part from his son. The bond between parents and children, paternal and filial attachment - they are still around. Obviously, during the 500 years, some things have changed while others have not. Some changes are pertinent to the matter at hand, other are not. To mention the obvious pertinent changes,
- Mathematics body grew dramatically.
- Technology changed beyond comparison.
We have computers, cheap drives, CD-ROMs, networks, the Web. Going to the extreme, it's tempting to suggest that, in a short while, there will not be need to send children anywhere, even for the sake of the most advanced instruction. The instruction will be available right at home with a huge selection to choose from.
Thirty years from now the big university campuses will be relics. Universities won't survive. It's as large a change as when we first got the printed book. Do you realize that the cost of higher education has risen as fast as the cost of health care? ... Such totally uncontrollable expenditures, without any visible improvement in either the content or the quality of education, means that the system is rapidly becoming untenable. Higher education is in deep crisis... Already we are beginning to deliver more lectures and classes off campus via satellite or two-way video at a fraction of the cost. The college won't survive as a residential institution.
For want of a better source, I'll extrapolate Drucker's words to cover the school system. The time will show whether his projection comes true or not and, if it does, to what extent. What is indubitable is that modern technology affords us more freedom in selecting ways and means of acquiring education.
Other things proved more stable and have not changed. (Murphy's Law is one example. Though unknown until recently, it is now accepted as an universal truth that held from the time immemorial. Some see in it a probable explanation for the Big Bang.) In education, there are several universal truths:
- The pedagogy is important.
- Motivation or the lack thereof depends on the prevailing culture.
- Differences in personal abilities affect both the process and the end result of education.
The lack of motivation is not peculiar to our times. When we look into the past, the natural tendency is to emphasize the progress made in mathematics, science and society as a whole. However, as an example, it is said that in "...early-nineteenth-century Germany ... a mathematician was essentially a poor drudge whose time was spent pumping basic calculations into ill-prepared unmotivated pupils..." [Fauvel et al]
Education needs a reform. But we should not feel bad about it.
- T.Dantzig, NUMBER: The Language of Science, The Free Press, 1954
- Möbius and his band, ed. J.Fauvel, R.Flood and R.Wilson, Oxford University Press, 1993